The terms "knowledge base" and "knowledge graphs" have gained a lot of popularity recent years, especially after Google's introduction about the Google Knowledge Graph. However, those terms have been used interchangeably and there has been lacking a good definition for distinguishing those terms.
Recently, the SEMANTiCS paper Towards a Definition of Knowledge Graphs from Ehrlinger, Lisa [2] provides a quite comprehensive analysis on those terms and a good definition about knowledge graph to define the distinction and relationships between those terms, which are quite useful.
"The knowledge base is a dataset with formal semantics that can contain different kinds of knowledge, for example, rules, facts, axioms, definitions, statements, and primitives" [1]
"A knowledge graph acquires and integrates information into an ontology (or knowledge base) and applies a reasoner to derive new knowledge."
More recently, Auer, Sören et al. relaxed the definition a little bit by any method instead of a reasoner when deriving new knowledge. That is,
"A knowledge graph acquires and integrates information into an ontology (or knowledge base) and applies a reasoner or other computaitonal methods to derive new knowledge."
This definition aligns with the assumption that a knowledge graph is somehow superior and more complex than a knowledge base (e.g., an ontology) because it applies a reasoning engine to generate new knowledge and integrates one or more information sources. Consequently, a manually created knowledge graph that does not support integration aspects is a plain knowledge base or knowledge-based system if it provides reasoning capabilities.
It is also interesting to note for me that an ontology consists not only of classes and properties (e.g., owl:ObjectProperty and owl:DatatypeProperty), but can also hold instances (i.e., the population of the ontology).
[1]. J. Davies, R. Studer, and P. Warren. Semantic Web Technologies: Trends and Research in Ontology-based Systems. John Wiley & Sons, 2006.
[2]. Ehrlinger, Lisa and Wolfram Wöß. Towards a Definition of Knowledge Graphs. SEMANTiCS conference, 2016.
[3]. Auer, Sören et al. Towards a knowledge graph for science, International Conference on Web Intelligence, Mining and Semantics, 2018.